All of a sudden ?
Screen is broken ? How ?
First: what is a basic cover ?
Second: Don't leave Kindles and other brakeable things at the bottom of a backpack, AND then pile kilo's & kilo's of HARD things, with sharp corners on top.
The Amazon covers ( only have the lighted one ), seems pretty sturdy, but I suspect even those could not protect the K3 in all situations.
Basically: Remember that the Kindle is sort of fragile, so DON'T keep it at the bottom of your backpack. Better get an other backpack with a different layout so your Kindle is better protected.

Pretty much it is in the pouch separated from the hard things but somehow the hard things manage to cause the screen to break. I was using it fine 3 hours before it broke and I placed it in my backpack (in that pouch in my backpack), came home and the screen was broken.

The screen was broken 3/4 and on the 1/4 left you only see lines moving when you are pressing the keys.

I've read so many threads here and elsewhere where Kindles end up broken in rucksacks - perhaps a combo of no or inadequate cover plus the fact that people are used to not treating rucksacks carefully - being swung here, thrown there and receiving knocks from all over.

I keep my Kindle in a over-the-shoulder bag when on the move - the Kindle fits quite snugly in one of the compartments and doesn't move around much. It's also kept in the lighted-cover which is quite a hard case.

I'm not sure what you mean OP by basic cover - but if you're taking your Kindle out and about a lot, a hard case will give the best protection. And perhaps a bag where the Kindle fits snugly and isn't going to get swung or knocked much.

I would get an aluminium case or some other metal, to transport the Kindle in, in a rucksack. I don't really think leather or other cases are sufficient to withstand the kind of forces your Kindle is subjected to when carrying it in a rucksack with a lot of books. Some say that it can be done, or they have done it with just a sturdy cover. In my opinion they've been lucky till sofar. I mean: I've seen my teenager throw her rucksack with expensive calculators and such in it around;you would't believe it. Or schoolmates that did it for her.
Or you could transport your Kindle, with a sturdy cover in a seperate bag, like Kindleworm says.

Just don't underestimate the forces that can work on your Kindle, if it's too tightly wedged between other things. These forces have to go somewhere-----takes the easiest route----which sometimes is the Kindle-screen. Take care.

I would get an aluminium case or some other metal, to transport the Kindle in,

That is what I do with my iPad when I expect it to experience rougher handling than my soft bag can protect it. It was one of those "bonus gift collection with purchase of $50 from Lancome" or some other makeup brand. I got a sheet of 1/4 inch foam at Hobby Lobby and cut it to size. The cords and a ballpoint pen go under the foam, and the ipadgoes on top (screen against the foam).

When I was using my 505, I got a nice plastic Rubbermaid container with a tight fitting lid. You don't need the lid to come off in your backpack and expose your Kindla to sharp heavy destruction. Then put in a foam layer or a couple of thick soft washcloths. You want something soft to pad it and stop it from slipping around inside the container.

Also, just a reminder to wear it against your skin under your coat in cold weather. No sudden glass-shattering changes of temps for it.

That is what I do with my iPad when I expect it to experience rougher handling than my soft bag can protect it. It was one of those "bonus gift collection with purchase of $50 from Lancome" or some other makeup brand. I got a sheet of 1/4 inch foam at Hobby Lobby and cut it to size. The cords and a ballpoint pen go under the foam, and the ipadgoes on top (screen against the foam).

When I was using my 505, I got a nice plastic Rubbermaid container with a tight fitting lid. You don't need the lid to come off in your backpack and expose your Kindla to sharp heavy destruction. Then put in a foam layer or a couple of thick soft washcloths. You want something soft to pad it and stop it from slipping around inside the container.

Also, just a reminder to wear it against your skin under your coat in cold weather. No sudden glass-shattering changes of temps for it.

I agree with that. I always have my Kindle in an Oberoncase (red Wild Roses), but I never, ever pack it in a backpack with heavy books.
But if I would, I'd pack it in some rigid, aluminium or hard plastic container.

This one from Klearkase, seems the same, but four times the price (and only for the K2). Does have a pic of someone spilling a latte on the Kindle in the case ... I don't suggest you do that, as it also seems not to completely cover the kindle.